Hi, You could buy a soil test kit.  I'm in Franklin County and our Extension office sells them.  Probably your Extension office does, too.  Here is their website:
https://extension.osu.edu/tuscarawas-county-office
That said, it will tell you what's wrong with your soil but I would guess that you may have a problem with the kinds of grass you have growing.  Maybe you have weedy grasses or warm season grasses that don't green up like the grasses we want to grow.  Could you send me some photos of your lawn including some close-ups of the different types of grass and I'll try to get them identified?  Also, if you grab the grass, can you pull it right out including the roots?  That would be a sign of grub damage.
(That's what I was doing earlier today).

Hi,
Thanks for the photos!  The more, the better.  The first photo is NOT of the problem area, right?  I see the area in the back yard that is less green than the rest. Is the close-up of the problem area?  When were those taken?  Did it ever green up as much as the rest of it?  And what does that area look like now?  Could you take a close-up of it now?
I am gathering info that I know my former turfgrass prof will ask.
Thanks,
Barb   

Where was the close-up taken?  In the problem area?

Hi, I've sent your question and some pics to my turfgrass professor and will get back to you with what he says.  I'm thinking it might be rough bluegrass in that area.  Here's some info about rough bluegrass:
https://www.extension.iastate.edu/turfgrass/blog/nick-christians/brown-areas-your-lawn-it-could-be-rough-bluegrass-poa-trivialis
Barb

Hi again,
Well, Dr. Gardner (Turfgrass and horticulture prof at OSU) got back to me and this is what he said:

"I’m inclined to think it’s a soil issue. The only closeup shows a mix of ryegrass and tall fescue and its probably the ryegrass that fades more than the tall fescue which is why the patch does not have dramatic borders and seems to have some green still in it. I don’t know what a soil test will tell him for this issue. If he takes a core out of the area that remains green and then a core out of the area that yellows out my guess is that the area that stays green will have more dark soil/organic matter compared to the other area which may be straight clay. What happens then is in the middle of summer the heavy clay areas have an infiltration capacity of about 0.07 inches per hour so keeping them wetted with run of the mill sprinklers can be very difficult – most of the water just runs off.

If this is the case, then the fix is long term in nature – topdressing and core aerification for several years or until an improvement is realized."

So - he identified the grasses in that close-up and they are not what I thought they were (rough bluegrass) but he has offered a long-term solution.  Let me know if you have any more questions and good luck.  Might I say, you have a large lawn and most of it is looks great!

Let me know if I can be of further assistance,

You're most welcome.  I appreciate Dr. Gardner being  able and willing to help,
Barb